Alglib

Functions
template<typename MatrixT , typename VectorT >
void	capd::alglib::computeEigenvalues (const MatrixT &A, VectorT &eigenRealPart, VectorT &eigenImPart)
	Function computes Eigenvalues of a general matrix. More...
template<typename MatrixT , typename VectorT >
void	capd::alglib::computeEigenvaluesAndEigenvectors (const MatrixT &A, VectorT &eigenRealPart, VectorT &eigenImPart, MatrixT &vectorRealPart, MatrixT &vectorImPart)
	Computes Eigenvalues and corresponding right Eigenvectors. More...
template<typename T >
std::string	capd::alglib::complexToString (const T &re, const T &im)
	Writes complex number to string in human readable form :) More...
template<typename VectorType >
std::string	capd::alglib::eigenvaluesToString (const VectorType &re, const VectorType &im, std::string separator=", ")
	Converts vector of eigenvalues to text (string) More...
template<typename MatrixType >
std::string	capd::alglib::eigenvectorsToString (const MatrixType &re, const MatrixType &im, std::string separator=", ", std::string vectorSeparator=",\n")
	Converts eigenvectors stored as columns of matrices to text (string) More...

Detailed Description

Function Documentation

complexToString()

template<typename T >

std::string capd::alglib::complexToString	(	const T &	re,
		const T &	im
	)

Writes complex number to string in human readable form :)

computeEigenvalues()

template<typename MatrixT , typename VectorT >

void capd::alglib::computeEigenvalues	(	const MatrixT &	A,
		VectorT &	eigenRealPart,
		VectorT &	eigenImPart
	)

Function computes Eigenvalues of a general matrix.

The algorithm finds eigenvalues of a general matrix by using the QR algorithm with multiple shifts.

Remarks

Nonrigorous! Works only for double matrices!

Input:

Parameters

[in]

A

square matrix

Output:

Parameters

[out]	eigenRealPart	vector of real parts of eigenvalues.
[out]	eigenImPart	vector of imaginary parts of eigenvalues.

computeEigenvaluesAndEigenvectors()

template<typename MatrixT , typename VectorT >

void capd::alglib::computeEigenvaluesAndEigenvectors	(	const MatrixT &	A,
		VectorT &	eigenRealPart,
		VectorT &	eigenImPart,
		MatrixT &	vectorRealPart,
		MatrixT &	vectorImPart
	)

Computes Eigenvalues and corresponding right Eigenvectors.

The algorithm finds eigenvalues and eigenvectors of a general matrix by using the QR algorithm with multiple shifts.

Remarks

Works only for double matrices and vectors!

Input:

Parameters

[in]

A

square matrix

Output:

Parameters

[out]	eigenRealPart	vector of real parts of eigenvalues.
[out]	eigenImPart	vector of imaginary parts of eigenvalues.
[out]	vectorRealPart	matrix whose i-th column is real part of eigenvector corresponding to i-th eigenvalue
[out]	vectorImPart	matrix whose i-th column is imaginary part of eigenvector corresponding to i-th eigenvalue

eigenvaluesToString()

template<typename VectorType >

std::string capd::alglib::eigenvaluesToString	(	const VectorType &	re,
		const VectorType &	im,
		std::string	separator = ", "
	)

Converts vector of eigenvalues to text (string)

Parameters

[in]	re	vector of real parts of eigenvalues
[in]	im	vector of imaginary parts of eigenvalues
[in]	separator	string that separates eigenvalues

Returns

eigenvalues in text format

eigenvectorsToString()

template<typename MatrixType >

std::string capd::alglib::eigenvectorsToString	(	const MatrixType &	re,
		const MatrixType &	im,
		std::string	separator = ", ",
		std::string	vectorSeparator = ",\n"
	)

Converts eigenvectors stored as columns of matrices to text (string)

Parameters

[in]	re	matrix of real parts of eigenvectors (as its columns)
[in]	im	matrix of imaginary parts of eigenvectors
[in]	separator	string that separates vectors coefficients
[in]	vectorSeparator	string that separates vectors (default is , )

Returns

eigenvectors in text format